I don't quite know how the American schooling system works, so I shall explain how it works for me in England.
I shall ignore primary school, for that is the young ages of 8 to 11 (years 3, 4, 5 & 6), and in that time you learn basic english maths and science and then you do whatever little kids do in school.
We start in Secondary school at the age of 11.
For the first three years that you spend at the school (Years 7, 8 & 9) you will learn a compulsory course.
This includes English, Maths, Science (Covering Biology, Chemistry and Physics), Art, ICT, an MFL (Moder Foreign Language, including French, German, Spanish and Italian), Religious Education, Drama, Physical Education and possibly other lessons that your school teaches.
For this moment, the lesson stuff is basic and is still similar to Primary school. Teaching might not be so much as teaching and more distracting you long enough for the school to lock you up for the day.
The lessons you do however are designed to give you enough education to take on qualifications in whatever subject you choose.
Compulsary courses, which I know definitely include English, Maths, Science, PE, RE, History, Geography, ICT and an MFL, are enforced by the Government as these are the things that the country deems it necesarry that you know of for multiple reasons. The English, Maths and Science are obvious. PE is to keep you fit. ICT and an MFL is because these are increasingly important in today's world and RE covers not just Religion, but things like love Education and Racial Equality and Citizenship.
History and Geography are equally important in letting you understand citizenship aswell as being important for future education or work.
Now, a student might be having a lesson that he has to do, like Drama, which he does not enjoy.
But that's okay, because he reaches his 4th year of Secondary Education and enters Year 10.
At this point, he chooses the subjects he wishes to learn.
These are more ranged than the lessons you had before. At this point, you enter into one of the lowest levels of qualifications readying you for the future, where you will either get a job or enter into tertiary education.
At this point there are some courses you still must take.
English Language, Double Science (Provides for 2 general science GCSEs), Mathematics, Religious Education, Physical Education (Does not have an exam, is for fitness only).
The MFL and ICT are removed as these may not suit you personally and it would be wasteful to force you to do try a full qualification of something which you are not good at. Some schools may force you to take one, however.
(My previous school was a "Community College" and as such focussed on MFL's and had a school policy that enforced the learning of atleast one MFL)
At this point however you get to choose to take usually 3 or 4 courses that you want.
This could be History, Drama, Geography, an MFL, ICT, PE (Examined on Physical ability and knowledge (basic biology)), Triple Science (Provides three specific Science GCSE's, one for Biology, one Chemistry and one Physics), Art, Design Technology (All sorts including Woodwork, Electronics and Textiles), Religious based classes, Politics in some schools, Music and many more.
At this point you partake in an education suited to your choices.
You spend two years doing these courses and recieve a GCSE at the end, a General Certificate of Secondary Education.
Following this, you are then out of compulsary education. You can go get a job, or an apprenticeship or go onto tertiary education, such as a College or Sixth Form.
At a College or Sixth Form you choose the subjects you want out of whatever options are available to you.
You will require specific grades in your GCSE's to qualify for the course, will not have to do any courses you don't wish to and are not legally required to be there.
It's the level of examination before University.
You work for A Levels (Usually, or a lower, possibly vocational qualification). You spend one year where you do a full course and at the end recieve an AS Level. If you continue into the next year with the course, you further onto an A Level, Advanced Certificate of Secondary Education.
From there it's onto University.
My main point of this is that you have a few compulsary lessons that you are forced to do because it is in your best interest.
Your government has designed courses for you that are to provide you with the necesarry education to survive in the real world, whether that's getting a job or not or continuing onto additional education.
You get to a point in your education where you get full reign of your education.
No longer do you have to learn what you did not want to or found too difficult. You learn for what you are ready to learn.
You just have to put up with the compulsary stuff for a few years.
Out of Secondary Education there are only 3 years out of 7 that I don't have a single-say in what I learn.
My countries education system might be different from yours, but it can't be that much so.